College dataset¶

# save default options and parameters

defop = options()

defpar = par(no.readonly=T)

​

# function to modify plot parameters

plot_pars = function(w=7,h=7) {options(repr.plot.width=w, repr.plot.height=h)}

# a) import data

fpath = file.path(getwd(),'datasets','College.csv')

college = read.csv(fpath)

​

dim(college)

head(college)

## alternatives

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## 1

# setwd("E:/Data Science/Statistics/Intro to Statistical Learning with R")

# df = read.csv("./datasets/College.csv")

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## 2

# download.file("https://statlearning.com/College.csv", destfile="College.csv", mode="wb")

# mode='wb' >> for windows

# df = read.csv("College.csv")

​

# head(df)

# missing values in data

sum(is.na(college))

# columns with missing values

names(college)[colSums(is.na(college)) > 0]

# rows with missing values

rownames(college)[apply(college, 1, function(x) sum(is.na(x))) > 0]

str(college)

# Create rownames from college names

rownames(college) = college[,1]

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# Remove column containing names

college = college[,-1]

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# Reclassify 'Private' as factor

college$Private = as.factor(college$Private)

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# Confirm changes

college[sample.int(nrow(college), 3), ]

# Summary of variables : 

#  numerical >> descriptive statistics

#  categorical >> frequency table

#  character >> count

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summary(college)

# factor columns

fcts = Filter(f = is.factor, college)

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# show levels

sapply(fcts, levels)

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# alternatively

# sapply(college[sapply(college, is.factor)], levels)

# Select variables for pairs plot

selected_vars = setdiff(names(college), c('F.Undergrad','P.Undergrad','Books',

                                          'S.F.Ratio','perc.alumni'))

length(selected_vars)

selected_vars

# increase plot size

plot_pars(17,17)

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# scatterplot matrix

pairs(college[,selected_vars], pch = 19,  cex = 0.5,

      lower.panel=, cex.labels=1.8)

​

# reset plot params

options(defop)

# High correlation relations

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# Correlation of numeric columns

corr = cor(college[sapply(college, is.numeric)])

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# Display |correlations| > 0.55

as.data.frame(apply(corr, 2, function(x) ifelse (abs(x) >=0.55, round(x,3), "-")))

# Correlation plot

suppressPackageStartupMessages(

library(corrplot))

​

plot_pars(9,8)

corrplot(cor(corr), method='number', tl.cex=1, number.cex=1)

​

options(defop)

library(ggplot2)

# Plot parameters

plot_pars(10,4)

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# Outstate vs Private boxplot

ggplot(college, aes(y=Private, x=Outstate, fill=Private)) + 

geom_boxplot() +

labs(title='Outstate distribution in Private and Non-private') +

​

theme_bw() +

theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),

      axis.text=element_text(size=14, face="bold"), 

      axis.title.x = element_text(size = 16),

      axis.text.x = element_text(size=15, angle=45, hjust=1))

​

# size=rel(3.5) to change all

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# reset plot dimensions

options(defop)

# Glance at Top10perc

plot.new()

par(mar=c(2,2,1,1))

par(oma=c(1,2,3,1))

plot_pars(17,5)

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par(fig=c(0,0.35, 0,1), new=TRUE)

hist(college$Top10perc, nclass='FD', col='thistle', cex.main=1.5, main='Histogram')

​

par(fig=c(0.35,1, 0,1), new=TRUE)

boxplot(Top10perc ~ Private, data=college, horizontal=T, col=5:6, 

        boxwex=0.3, frame=F, 

        main="Top10perc in Private v Non-Private", cex.main=1.5,

        ylab="Private", names=c('Private','Non-Private'), las=1,

        xlab="Top10perc Distribution")

​

# mtext("Top10perc", side=3, adj=0.40, cex=1.8, line=0, outer=TRUE)

title('Top10perc', adj=0.4, cex.main=2, line=1, outer=T)

​

options(defop)

# Create new variable 'Elite'

college$Elite = as.factor(ifelse(college$Top10perc > 50, 'Yes', 'No'))

summary(college$Elite)

# Elite and private

sum(college$Elite=="Yes")

sum(college$Elite=='Yes' & college$Private=='Yes')

college[sample.int(nrow(college), 3), ]

# Outstate Tuition - Elite

plot_pars(15,4)

boxplot(Outstate ~ Elite, data=college, horizontal=T, col=5:6, frame=F,

       main="Outstate Tuition in Elite v Non-elite", boxwex=0.5, las=1,

        ylab="Elite", xlab="Outstate tuition (USD)")

options(defop)

# Total student expenditure (with and without Outstate tuition)

# Student exp = Room.Board + Books + Personal + Outstate

​

college$TExp.without.O = college$Room.Board + college$Books + college$Personal

college$TExp.with.O = college$Outstate + college$Room.Board + college$Books + college$Personal

"a) Student expenditure related variables"

# selected variables

vars = c(unlist(strsplit('Outstate, Room.Board, Books, Personal, TExp.without.O, TExp.with.O, Expend', 

                         split=', ')))

xlabels = vars

ylabels = rep('Freq', 7)

​

# 2 by 3 grid

par(mfrow = c(3,3))

par(mar=c(5.1, 4.1, 4.1+2, 2.1))  # b,l,t,r

par(oma=c(0,0+2,0,0))

​

# resize plot params

plot_pars(17,15)

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# function to generate hist

for (i in seq(length(vars))) {

    var = vars[i]

    hist(college[, var], nclass='FD', col=c(i+1),

        main=paste(var), xlab=xlabels[i], ylab=ylabels[i],

        cex.main=2, cex.lab=1.7, cex.axis=1.5)

    median.var = median(college[, var])

    mtext(paste('median : ', median.var), 3, adj = 0.5, line = 0.5, cex=1.2, col=)

    abline(v=median.var, lty=2, lwd=2)

}

​

par(defpar)

options(defop)

# boxplots - Student expenses with and without Outstate tuition

plot_pars(17,4)

par(oma=c(0,0+1,0,0))

​

boxplot(college[tail(names(college), 2)], horizontal=T, col=5:6,

        main='Student expenses with and without Outstate tuition',

        xlab='Total Student Exp (Room.Board + Book + Personal)',

        ylab='Outstate Tuition', names=c('without','with'), las=0,

        boxwex=0.5, cex.lab=1.5, cex.axis=1.3, cex.main=1.7, frame=F)

​

par(defpar)

options(defop)

# Skewness and Kurtosis

suppressPackageStartupMessages(

library(psych))

​

t(round(describe(college[vars])[,c('skew','kurtosis')], 4))

"b) Faculty and student related ratios"

# selected variables

vars = c(unlist(strsplit('PhD Terminal S.F.Ratio perc.alumni Grad.Rate', split=' ')))

xlabels = vars

​

par(mfrow=c(2,3))

par(mar=c(5.1, 4.1, 4.1+2, 2.1))  # b,l,t,r

par(oma=c(0,0+2,0,0))

plot_pars(15,10)

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for (i in seq(length(vars))) {

    var = vars[i]

    hist(college[,var], nclass='FD', col=i+1,

        main=var, xlab=xlabels[i], ylab='Freq', 

         cex.main=2, cex.lab=1.6, cex.axis=1.5)

    median.var = median(college[, var])

    mtext(paste('median : ', median.var), 3, adj = 0.5, line = 0.5, cex=1.2)

    abline(v=median.var, lty=2, lwd=2)

}

​

par(defpar)

options(defop)

# Institutions with PhD > 100

cbind(rownames(college)[which(college$PhD > 100)], college[which(college$PhD > 100), 'PhD'])

## Graduation rate

summary(college$Grad.Rate)

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## No. of Istitutions with graduation rate < 50%

length(which(college$Grad.Rate < 50))

## % of Istitutions with graduation rate < 50%

round(137/nrow(college)*100, 2)

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# alternatively

# percentile = ecdf(college$Grad.Rate)

# percentile(49.99)*100

# Donor alumnis

summary(college$perc.alumni)

# Proportion of Private

a = data.frame(table(college$Private))

names(a) = c('Private', 'Count')

a$Prop = round(prop.table(table(college$Private)), 3)

a$Median.Personal = tapply(college$Personal, college$Private, median)

a[,'>1649'] = tapply(college$Personal, college$Private, function(x) sum(x > 1649))

a

# Histograms

par(mfrow=c(1,2))

par(oma=c(0,0+1,0,0))

plot_pars(10,4)

hist(college$Personal[college$Private=='Yes'], col=5, cex.main=1.5, cex.lab=1.3, cex.axis=1.2, 

     las=1, main='Personal exp in Private', xlab='Personal Exp', ylab='freq', nclass='FD')

hist(college$Personal[college$Private!='Yes'], col=6, cex.main=1.5, cex.lab=1.3, cex.axis=1.2, 

     las=1, main='Personal exp in Non-Private', xlab='Personal Exp', ylab='freq', nclass='FD')

par(defpar)

options(defop)

# Boxplot - Student personal exp in Private v Non-private

par(oma=c(0,0+1,0,0))

plot_pars(10,4)

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boxplot(Personal ~ Private, data=college, horizontal=T, col=5:6, 

       main='Personal exp in Private v Non-private', las=1,

       cex.main=1.7, cex.lab=1.5, cex.axis=1.2, frame=F)

​

par(defpar)

options(defop)